Medieval cosmology meets modern mathematics

A modern computer simulation shows a two-dimensional cross section of celestial spheres produced in a process suggested by 13th century scholar Robert Grosseteste. With certain specific values plugged in for quantities such as the intensity of light and the strength of interaction between light and matter, the simulation produced nine “perfect” spheres surrounding an imperfect realm of terrestrial matter, just as medieval cosmologists envisioned.

When imagining medieval Europe, most people envision knights and castles and maybe cathedrals. Science is usually nowhere in the picture. Apart from monks copying manuscripts, intellectual activity in the Middle Ages was supposedly on the same level as that of 21st century politicians.

But actually, a few medieval minds were busy building modern science’s foundations. Some sophisticated thinkers realized that nature should be understandable using human reason rather than superstition. One of the earliest such scholars was Robert Grosseteste.

An Oxford-educated English clergyman who in 1235 became the bishop of Lincoln, Grosseteste believed deeply that faith could be reconciled with reason. So he sought rational explanations for the natural world. He advocated the use of observation and experiment. He even recognized the value of theory. In considering a possible explanation for a fact, he said, you could perform observations or check your explanation against a theory that had previously been confirmed by observations. It was advanced scientific philosophy for the early 13th century.

Grosseteste’s own theorizing encompassed most of the natural world. Besides his prodigious writings on theology, he wrote about sound and heat, comets and rainbows. He was an authority on optics and extended his interest in light to the study of cosmology. He proposed a scheme to explain the entire Aristotelian cosmos — the series of concentric spheres on which the planets and stars supposedly rotated around the Earth. Those spheres embodied perfection and harmony; their rotations generating the “music of the spheres” that nobody heard. Grosseteste attempted to describe how those spheres had been created.

Nowadays, that task would require physicists to compose equations full of Greek letters corresponding to various physical quantities obeying laws of motion and interaction. Grosseteste appreciated the need to apply math to nature, but today’s elaborate mathematics was not available to him. Nonetheless he described his idea precisely enough for modern physicists to express it mathematically. And in fact, an international, interdisciplinary team of medievalists, linguists and scientists has actually translated Grosseteste’s words into modern mathematics. It turns out that his theory really is amenable to mathematical rigor.

Grosseteste began with the premise that light is the primal substance in the universe, the power that gives the cosmos shape and form. Light has the ability to spread from its origin in all directions. In so doing, Grosseteste reasoned, it created three-dimensional space from nothing. Grosseteste further assumed that light interacted with matter so as to drag it along for the ride. In the beginning, then, light burst the universe into existence and drove matter outward — a picture superficially similar to modern cosmology’s Big Bang theory.

As matter spread outward, its density would diminish. But it could not diminish forever, because that would lead to zero density — a vacuum, which nature (everybody then believed) abhorred. At some minimum density, matter’s expansion could continue no longer, so it formed a spherical shell with a “perfect” ratio of light to matter. Call it the firmament.

Next, Grosseteste proposed, light from the first sphere shone inward, pushing matter into a second spherical shell (this one presumably carrying the stars). And then the process would begin again, each sphere forming when conditions reached the perfect light-to-matter density ratio.

Eventually, though, the process would fail to produce that perfect ratio, leaving the matter of the Earth, at the center of all the spheres, in an imperfect state. Apparently light from the innermost sphere, containing the moon, did not possess sufficient oomph to create another perfect sphere.

Obviously, today’s view of the universe does not resemble Grosseteste’s version. But that’s not the issue. Physicist Richard Bower and collaborators are more interested in whether Grosseteste’s theory is capable of intelligible mathematical expression. And it is.

“We express Grosseteste’s model of how light interacts with matter in terms of modern mathematics and show that it can indeed generate his claimed structure of the Universe,” Bower and colleagues write in a new paper, online at arXiv.org.

Their math incorporates several subtle complications, but in essence is based on just a few key quantities. Most important is the strength of the interaction between light and matter. Other crucial factors include the opacity of the matter and the intensity of the light.

A first computer run of the equations seemed to work, except that it produced too many spheres. (There should be only nine beneath the firmament.) But that result assumed that all the spheres were completely transparent. Grosseteste’s writings do not require such transparency, though. Making the interior spheres less than perfectly transparent does the trick, lowering the light intensity as it gets closer to Earth.

“Such conditions can lead to the intensity dropping sufficiently so that the perfection process stalls. This is the type of universe in which Grosseteste imagines we live,” Bower and colleagues write.

There’s a curious catch to this success, though. Equations implementing Grosseteste’s theory produce the proper number of spheres only for a very narrow range of values of the key quantities. Light intensity must be very high, for instance. The interaction strength between light and matter must be at just the right level.

It’s in this regard that Grosseteste’s universe resembles cosmology today. To produce the cosmos that astronomers observe — with galaxies and stars, planets and people — certain physical quantities must be fine-tuned to values that can’t (at the moment) be easily explained. One possible explanation (simultaneously popular and unpopular) contends that multiple universes exist, with different combinations of values for the key quantities. Ours is the one with the combination that permits us to exist, just as Grosseteste’s was the one where the key quantities conspired to produce the right number or spheres. So his model was deeper than he realized — it, too, could have produced a multiverse, had he possessed the proper mathematical tools and a Macintosh. Without realizing it, he proposed a mechanism capable of creating a multiverse, just as today’s best cosmological theories do.

“We cannot know Grosseteste’s view,” write Bower and collaborators, “but the computer simulations have revealed a fascinating depth to his model of which he was certainly unaware.”

Grosseteste’s specific model of the cosmos does not, of course, correspond to the picture that physicists paint of it today. But in one respect, one of his deeper insights does resonate with modern scientists – his belief in the unity in nature. Today virtually all scientists agree that science seeks a unified understanding of nature, that the facts about the world are not separate and independent, but all part of a seamless mosaic underlying a reality accessible to reason. Grosseteste was one of the first to articulate that vision.

“Truly Grosseteste was one of the great encyclopedic thinkers of the world,” a 19th century biographer wrote, “and one who … must be ranked among the foremost who have sought to reduce diversity to unity, and to survey the whole extent of what is knowable, with the aid of observation and experiment, and in the light of all-embracing principles.”